Angular Momentum operators

Hi, my problem is with part two of the question I've attached. I'm not exactly sure what they are expecting me to do, is it simply calculating the expectation value of L_z , from the wavefunction given (i.e. cos(φ))

Not sure what part you have a problem with. I am assuming the 2nd paragraph. They basically want you to decompose the cosine into a superposition of eigenfunctions. The magnitude squared of the coefficients for each eigenfunction will give you the probability of that state.

Not sure what part you have a problem with. I am assuming the 2nd paragraph. They basically want you to decompose the cosine into a superposition of eigenfunctions. The magnitude squared of the coefficients for each eigenfunction will give you the probability of that state.

Oh yes, forgot about decomposing cosine and sine.

I got another question, which is, if given a wave function like

u = Acosine(Pi/2a) + B sin(Pix/a)

How would I sketch the form of this squared (i.e. the probability distribution)?